1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
astraxan [27]
3 years ago
6

How do you find the x intercepts of 3x^(5/3) - 4x^(7/3)

Mathematics
2 answers:
kaheart [24]3 years ago
7 0
Set the whole expression = to 0 and solve for x.

3x^(5/3) - 4x^(7/3) = 0.  Factor out x^(5/3):     x^(5/3) [3 - 4x^(2/3)] = 0

Then either x^(5/3) = 0, or 3 - 4x^(2/3) = 0.

In the latter case, 4x^(2/3) = 3. 

To solve this:  mult. both sides by x^(-2/3).  Then we have

4x^(2/3)x^(-2/3) = 3x^(-2/3),            or 4 = 3x^(-2/3).  It'd be easier to work with this if we rewrote it as

4           3
---  = --------------------
1            x^(+2/3)

Then 

4
---  = x^(-2/3).  Then, x^(2/3) = (3/4), and x = (3/4)^(3/2).  According to my     3                      calculator, that comes out to x = 0.65 (approx.)

Check this result!  subst. 0.65 for x in the given equation.  Is the equation then true?

My method here was a bit roundabout, and longer than it should have been.  Can you think of a more elegant (and shorter) solution?
Varvara68 [4.7K]3 years ago
7 0
To the risk of sounding redundant, as Altavistard already pointed out above

\bf 3x^{\frac{5}{3}}-4x^{\frac{7}{3}}=0\implies \stackrel{common~factor}{x^{\frac{5}{3}}}(3-4x^{\frac{2}{3}})=0\\\\
-------------------------------\\\\
x^{\frac{5}{3}}=0\implies \boxed{x=0}\\\\
-------------------------------\\\\
3-4x^{\frac{2}{3}}=0\implies 3=4x^{\frac{2}{3}}\implies (3)^3=\left(4x^{\frac{2}{3}}\right)^3
\\\\\\
27=64x^2\implies \cfrac{27}{64}=x^2\implies \sqrt{\cfrac{27}{64}}=x\implies \boxed{\cfrac{3\sqrt{3}}{4\sqrt{4}}=x}
\\\\\\
0.64951905283832898507\approx x
You might be interested in
This is from my algebra, is x/2 equal to -2x
slega [8]

No, because x/2 divides x by two, while -2x multiplies x by -2.

6 0
3 years ago
Solve the question: 3(.5y-6)=12​
makvit [3.9K]

Answer:

y = 20.

Step-by-step explanation:

Distribute:

3(0.5y)-3(6)=12

1.5y-18=12

Add 18 to both sides:

1.5y-18+18=12+18

1.5y=30

Solve for y:

\frac{1.5y}{1.5}=\frac{30}{1.5}

y=20

6 0
3 years ago
The weather forecaster says that there is a 51% chance of rain today. Which statement describes the likelihood that it will rain
vaieri [72.5K]

Answer:

It is neither likely nor unlikely that it will rain today.

Step-by-step explanation:


3 0
3 years ago
Randy has 53 inches of ribbon that he cuts into 8 pieces of equal length. What is the length of each piece of ribbon, in inches?
maw [93]

Answer:

6.625 inches or 6 5/8 inches

and the drop down hopefully will let you choose "between 6 and 7 inches"

Step-by-step explanation:

53/8 = 6.625

0.625 = 5/8

Let me know if you have questions about this. Have a good night.

6 0
2 years ago
A cyclist travels at a rate of 1.8 kilometers per minutes.how fat will the cyclist travel in 48 minutes?
WARRIOR [948]
You would multiply 1.8 × 48 to find your answer.

1.8
×48
--------
14.4
+72.0
--------
86.4

So the cyclist travels 86.4 km
4 0
3 years ago
Other questions:
  • A ramp is 17 ft long , rises 8 ft above the floor, and covers a horizontal distance of 15 ft,as shown in the figure
    5·1 answer
  • In a division problem the ____ is the original number, which is being divided by the divisor, to get the quotient.
    6·2 answers
  • Simplify.11^10/11^3 x 11^5
    6·2 answers
  • if an earthquake is 121,000 times as intense as the minimum detected earthquake, what is its richter number?
    15·1 answer
  • Smoe brought a bag of bird food that held 2 1/2 lbs. of food. He Fed Smoe Dog the same amount of food for each 12 days. How many
    12·1 answer
  • THe question is down below in the epic image
    11·1 answer
  • Y &lt; 5x – 2<br> What’s the solution?
    6·1 answer
  • Please help anyone PLSSSSS with my questions anyone can help me and plsss no links and pls with whole procedure pls
    7·1 answer
  • The price of a printer increased by 8% to $777.60. Find the usual price of the printer.
    8·1 answer
  • Help me with my homework​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!